本文研究離散時間、線性、非時變正值系統之動態輸出回授H∞控制器設計問題。首先針對輸出矩陣具有特定形式之正值系統，本文推導出以線性矩陣不等式（linear matrix inequality, LMI）與線性不等式組成之充要條件，其甚至適用於控制器為降階與具結構限制的情形。針對更具一般性之正值系統，本文提出相似的充分條件以及兩階段式之設計演算法。另外，更進一步地以類似論點延伸至另一種狀態空間之控制器合成問題。最後，模擬結果證實了本文所提方法是有效的。

This paper is concerned with the H-infinity dynamic output-feedback stabilization of discrete-time positive linear time-invariant systems. It is first shown that for a class of positive systems whose output matrix has a particular form, necessary and sufficient condition is derived in terms of a set of linear matrix inequality (LMI) and linear inequalities, even if the output feedback controllers are of reduced-order and/or have structural constraints. Analogously, for the more general case, sufficient conditions of similar form are also derived and a two-stage algorithm is developed. Further extension to the synthesis problem in a different state space is also made by similar arguments. Finally, simulation is conducted that establishes the effectiveness of the proposed methods.

目錄
中文摘要 I
ABSTRACT II
目錄 III
圖目錄 V
表目錄 VI
符號說明 VII
第1章 緒論 1
1.1 文獻回顧 1
1.2 研究動機與研究目標 2
1.3 論文架構 3
第2章 背景知識 4
第3章 正值系統之H∞控制器設計Ⅰ 7
3.1 問題敘述 7
3.2 正值系統之H∞控制器設計Ⅰ（情況一） 9
3.2.1 H∞性能設計條件 9
3.2.2 正值特性設計條件 13
3.3 正值系統之H∞控制器設計Ⅰ（情況二） 16
3.3.1 矩陣T1之設計 21
3.4 正值系統之H∞控制器設計Ⅰ（情況三） 26
第4章 正值系統之H∞控制器設計Ⅱ 29
4.1 系統狀態轉換 29
4.2 正值系統之H∞控制器設計Ⅱ（情況一） 32
4.2.1 H∞性能設計條件 32
4.2.2 正值特性設計條件 37
4.3 正值系統之H∞控制器設計Ⅱ（情況二） 40
第5章 模擬結果與討論 47
5.1 萊斯利模型 47
5.2 模擬例子一 49
5.2.1 正值系統之H∞控制器設計Ⅰ 50
5.2.2 正值系統之H∞控制器設計Ⅱ 53
5.3 模擬例子二 54
5.3.1 正值系統之H∞控制器設計Ⅰ 55
5.3.2 正值系統之H∞控制器設計Ⅱ 56
5.4 模擬例子三 57
5.4.1 正值系統之H∞控制器設計Ⅰ 58
5.4.2 正值系統之H∞控制器設計Ⅱ 60
5.5 模擬例子四 61
5.5.1 正值系統之H∞控制器設計Ⅰ 62
5.5.2 正值系統之H∞控制器設計Ⅱ 64
第6章 結論與未來研究方向 67
參考文獻 69
附錄 74

圖目錄
圖3.1 系統架構 7
圖3.2 含有延遲函數F之系統架構 26
圖3.3 廣義受控體P-bar之系統架構 27
圖5.1 閉迴路系統波德圖 51
圖5.2 干擾訊號w(k)時域響應圖 51
圖5.3 狀態x1(k)時域響應圖 52
圖5.4 狀態x2(k)時域響應圖 52
圖5.5 狀態x3(k)時域響應圖 53

表目錄
表1 例子之比較 47

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